PROJECT SUMMARY Proteins are the machines that carry out the chemical reactions necessary for life. Unlike man-made machines, proteins exhibit a unique combination of features: high performance with respect to specific biological functions, and adaptability to changes in their environment. The coincidence of these two properties suggests that there exist yet-unknown design principles which govern evolved machines. However, despite the clear implications of this observation for our understanding of evolution, proteins, and engineering, these design principles remain elusive due to the high-dimensionality of internal protein atomic motions and wide range of length- and time-scales associated with the problem. At present, molecular dynamics simulations have been the most useful tools for shedding light on the internal dynamics of proteins, but given the challenge in measuring the time-dependent internal motions a protein undergoing some biological process, these simulations are often not confirmable by experimental data. New experiments and analysis methods in our lab are able to measure internal motions within proteins at Angstrom-resolution. This provides an opportunity: I will carry out substantial experimentally-verified molecular dynamics simulations which model the new experiments. By carrying out these simulations using several different force fields and comparing a variety of quantities to their experimental values, I will construct new experimentally-motivated molecular dynamics ?best practices? such that simulations and experiment imply consistent properties of the given protein. Using these ?optimized? molecular dynamics methods along with data analysis methods such as dimensional reduction, I will study protein dynamics in multiple contexts, including electric-field stimulated X-ray crystallography (EFX), a novel technique by which an electric field is applied to a protein crystal and the resulting structure is measured using X-ray crystallography, and room-temperature X-ray crystallography (RTX), a new way of determining thermal ensembles of protein configurations at room temperature using static crystallography data. These will enable me to reduce the measurements of atomic-scale motions of thousands of individual atoms to a description of coordinated motions on different scales with the expectation of revealing a small number of mechanical mechanisms dictating protein function and allostery. This mathematical analysis not only opens up new experimental, computational and conceptual methods for understanding protein function from microscopic structural information; its improved, evidence-based simulation methods can be used for predicting collective motions when crystallography experiments are nonexistent or inaccessible. Overall, this research will develop new quantitative tools for studying the connection between protein mechanics and function, and implement these tools to extract a low-dimensional, ordered description of this seemingly high-dimensional, disordered phenomenon.